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A014659 Odd numbers that do not divide 2^k + 1 for any k >= 1. 4

%I #24 Feb 18 2021 01:32:24

%S 7,15,21,23,31,35,39,45,47,49,51,55,63,69,71,73,75,77,79,85,87,89,91,

%T 93,95,103,105,111,115,117,119,123,127,133,135,141,143,147,151,153,

%U 155,159,161,165,167,175,183,187,189,191,195,199,203,207,213,215,217,219

%N Odd numbers that do not divide 2^k + 1 for any k >= 1.

%C This is the subset of odd integers > 1 as (2*n - 1) in A179480 such that A179480(n) is even. Example: A179480(18) = 6, even; corresponding to (2*18 - 1), 35. Then 35 is in A014659. A014657 is the subset of odd terms > 1 corresponding to odd terms in A179480. - _Gary W. Adamson_, Aug 20 2012

%C From _Wolfdieter Lang_, Aug 22 2020: (Start)

%C These odd numbers are the moduli named 2*n+1 in the definition of A003558(n), for n >= 1, for which the + sign applies. The signs in the definition of A003558 are given in A332433.

%C These are the odd numbers N >= 3 for which A003558((N-1)/2) = A002326((N+1)/2), the period length P(N) of the cycles {2^k (mod N)}_{k=0}^(P(N)-1). Compare the periods given in A201908((N+1)/2, k). (End)

%H T. D. Noe, <a href="/A014659/b014659.txt">Table of n, a(n) for n = 1..1000</a>

%H P. Moree, <a href="https://doi.org/10.1006/ffta.1996.0172">Appendix B</a>, to V. Pless et al., Cyclic Self-Dual Z_4 Codes, Finite Fields Applic., vol. 3 pp. 48-69, 1997.

%Y Cf. A179480, A002326, A003558, A201908, A332433.

%Y Cf. A014657, numbers that divide 2^k + 1 for some k.

%K nonn

%O 1,1

%A _N. J. A. Sloane_

%E More terms from _Don Reble_, Nov 03 2001

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Last modified April 25 08:27 EDT 2024. Contains 371964 sequences. (Running on oeis4.)